使用功能时间序列数据的 entropy 和 ergodic 属性进行尺度对函数模式估计
Mohammed B Alamari1, Fatimah A Almulhim2, Ibrahim M Almanjahie1
1Department of Mathematics, College of Science, King Khalid University, Abha 62223, Saudi Arabia.
Entropy (Basel, Switzerland)
|June 26, 2025
概括
这项研究引入了一个新的递归L1估计器,用于假度空间中的条件模式,为混合过程提供了一个强大的替代方案. 拟议的方法在模拟和现实数据分析中表现出卓越的性能.
科学领域:
- 统计 统计 统计 统计
- 时间序列分析时间序列分析
- 功能数据分析 功能数据分析
背景情况:
- 条件模式的标准估计器通常依赖于混合过程,这可能是数学上复杂的.
- 厄戈迪性提供了一个更易于处理的假设,以科尔莫戈罗夫-西奈为特征,反映了过程动态和波动.
- 函数时间序列 (fts) 由于其复杂的数学属性而存在独特的挑战.
研究的目的:
- 为条件模式开发和分析一种新的递归L1估计器.
- 在输入变量处于伪度空间时调查估计器的属性.
- 为现有方法提供一个强大的替代方案,使用一个ergodicity假设.
主要方法:
- 在功能时间序列的ergodicity假设下构建递归L1估计器.
- 非对称性属性的导出,包括收率和Borel-Cantelli (BC) 一致性.
- 将收率专注于独立案例,核心方法和向量值场景.
主要成果:
- 拟议的递归L1估计器被证明是异象一致的 (BC一致).
- 对于各种功能时间序列设置,可得出特定的收率.
- 数字实验证实了估计器对现有方法的优越性.
结论:
- 新的递归L1估计器为伪度空间的条件模式估计提供了强大的和有效的方法.
- 厄尔戈迪性在功能时间序列分析中为混合假设提供了一种实用且数学上合理的替代方案.
- 估计器在模拟和真实数据上的强表现验证了它的实用性.
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